Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20286170 | C2 | semidirect |
| 2. #20276646 | C2 | semidirect |
| 4. #20275972 | C2 | semidirect |
| 5. #20272732 | C2 | semidirect |
| 6. #20272656 | C2 | semidirect |
| 7. C53×#1349 | C2 | semidirect |
| 166. #1349 | D53 | semidirect |
| 193. C53 | #12166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286170 | 2 |
| #20276646 | 2 |
| #20276626 | 2 |
| #20275972 | 2 |
| #20272732 | 2 |
| #20272656 | 2 |
| C53×#1349 | 2 |
| #12166 | 53 |